PSSE Redux: Convex Relaxation, Decentralized, Robust, and Dynamic Approaches

This chapter aspires to glean some of the recent advances in power system state estimation (PSSE), though our collection is not exhaustive by any means. The Cram{\'e}r-Rao bound, a lower bound on the (co)variance of any unbiased estimator, is first derived for the PSSE setup. After reviewing the classical Gauss-Newton iterations, contemporary PSSE solvers leveraging relaxations to convex programs and successive convex approximations are explored. A disciplined paradigm for distributed and decentralized schemes is subsequently exemplified under linear(ized) and exact grid models. Novel bad data processing models and fresh perspectives linking critical measurements to cyber-attacks on the state estimator are presented. Finally, spurred by advances in online convex optimization, model-free and model-based state trackers are reviewed.Comment: 43 Pages, 8 figure

Smart Grid Monitoring Using Power Line Modems: Anomaly Detection and Localization

The main subject of this paper is the sensing of network anomalies that span from harmless impedance changes at some network termination to more or less pronounced electrical faults, considering also cable degradation over time. In this paper, we present how to harvest information about such anomalies in distribution grids using high frequency signals spanning from few kHz to several MHz. Given the wide bandwidth considered, we rely on power line modems as network sensors. We firstly discuss the front-end architectures needed to perform the measurement and then introduce two algorithms to detect, classify and locate the different kinds of network anomalies listed above. Simulation results are finally presented. They validate the concept of sensing in smart grids using power line modems and show the efficiency of the proposed algorithms.Comment: A version of this paper has been accepted for publication in IEEE Transactions on Smart Grid

Review of Smart Meter Data Analytics: Applications, Methodologies, and Challenges

The widespread popularity of smart meters enables an immense amount of fine-grained electricity consumption data to be collected. Meanwhile, the deregulation of the power industry, particularly on the delivery side, has continuously been moving forward worldwide. How to employ massive smart meter data to promote and enhance the efficiency and sustainability of the power grid is a pressing issue. To date, substantial works have been conducted on smart meter data analytics. To provide a comprehensive overview of the current research and to identify challenges for future research, this paper conducts an application-oriented review of smart meter data analytics. Following the three stages of analytics, namely, descriptive, predictive and prescriptive analytics, we identify the key application areas as load analysis, load forecasting, and load management. We also review the techniques and methodologies adopted or developed to address each application. In addition, we also discuss some research trends, such as big data issues, novel machine learning technologies, new business models, the transition of energy systems, and data privacy and security.Comment: IEEE Transactions on Smart Grid, 201

Distributed Monitoring of Voltage Collapse Sensitivity Indices

The assessment of voltage stability margins is a promising direction for wide-area monitoring systems. Accurate monitoring architectures for long-term voltage instability are typically centralized and lack scalability, while completely decentralized approaches relying on local measurements tend towards inaccuracy. Here we present distributed linear algorithms for the online computation of voltage collapse sensitivity indices. The computations are collectively performed by processors embedded at each bus in the smart grid, using synchronized phasor measurements and communication of voltage phasors between neighboring buses. Our algorithms provably converge to the proper index values, as would be calculated using centralized information, but but do not require any central decision maker for coordination. Modifications of the algorithms to account for generator reactive power limits are discussed. We illustrate the effectiveness of our designs with a case study of the New England 39 bus system.Comment: 10 pages, submitted for publicatio

Low-Resolution Fault Localization Using Phasor Measurement Units with Community Detection

A significant portion of the literature on fault localization assumes (more or less explicitly) that there are sufficient reliable measurements to guarantee that the system is observable. While several heuristics exist to break the observability barrier, they mostly rely on recognizing spatio-temporal patterns, without giving insights on how the performance are tied with the system features and the sensor deployment. In this paper, we try to fill this gap and investigate the limitations and performance limits of fault localization using Phasor Measurement Units (PMUs), in the low measurements regime, i.e., when the system is unobservable with the measurements available. Our main contribution is to show how one can leverage the scarce measurements to localize different type of distribution line faults (three-phase, single-phase to ground,..) at the level of sub-graph, rather than with the resolution of a line. We show that the resolution we obtain is strongly tied with the graph clustering notion in network science

Low-Resolution Fault Localization Using Phasor Measurement Units with Community Detection

A significant portion of the literature on fault localization assumes (more or less explicitly) that there are sufficient reliable measurements to guarantee that the system is observable. While several heuristics exist to break the observability barrier, they mostly rely on recognizing spatio-temporal patterns, without giving insights on how the performance are tied with the system features and the sensor deployment. In this paper, we try to fill this gap and investigate the limitations and performance limits of fault localization using Phasor Measurement Units (PMUs), in the low measurements regime, i.e., when the system is unobservable with the measurements available. Our main contribution is to show how one can leverage the scarce measurements to localize different type of distribution line faults (three-phase, single-phase to ground, ...) at the level of sub-graph, rather than with the resolution of a line. We show that the resolution we obtain is strongly tied with the graph clustering notion in network science.Comment: Accepted in IEEE SmartGridComm 2018 Conferenc

Distributed Robust Power System State Estimation

Deregulation of energy markets, penetration of renewables, advanced metering capabilities, and the urge for situational awareness, all call for system-wide power system state estimation (PSSE). Implementing a centralized estimator though is practically infeasible due to the complexity scale of an interconnection, the communication bottleneck in real-time monitoring, regional disclosure policies, and reliability issues. In this context, distributed PSSE methods are treated here under a unified and systematic framework. A novel algorithm is developed based on the alternating direction method of multipliers. It leverages existing PSSE solvers, respects privacy policies, exhibits low communication load, and its convergence to the centralized estimates is guaranteed even in the absence of local observability. Beyond the conventional least-squares based PSSE, the decentralized framework accommodates a robust state estimator. By exploiting interesting links to the compressive sampling advances, the latter jointly estimates the state and identifies corrupted measurements. The novel algorithms are numerically evaluated using the IEEE 14-, 118-bus, and a 4,200-bus benchmarks. Simulations demonstrate that the attainable accuracy can be reached within a few inter-area exchanges, while largest residual tests are outperformed.Comment: Revised submission to IEEE Trans. on Power System

Decentralized consensus finite-element Kalman filter for field estimation

The paper deals with decentralized state estimation for spatially distributed systems described by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. A fully scalable approach is pursued by decomposing the domain into overlapping subdomains assigned to different processing nodes interconnected to form a network. Each node runs a local finite-dimensional Kalman filter which exploits the finite element approach for spatial discretization and the parallel Schwarz method to iteratively enforce consensus on the estimates and covariances over the boundaries of adjacent subdomains. Stability of the proposed distributed consensus-based finite element Kalman filter is mathematically proved and its effectiveness is demonstrated via simulation experiments concerning the estimation of a bi-dimensional temperature field.Comment: 19 pages, 9 figure

Finite-time Guarantees for Byzantine-Resilient Distributed State Estimation with Noisy Measurements

This work considers resilient, cooperative state estimation in unreliable multi-agent networks. A network of agents aims to collaboratively estimate the value of an unknown vector parameter, while an {\em unknown} subset of agents suffer Byzantine faults. Faulty agents malfunction arbitrarily and may send out {\em highly unstructured} messages to other agents in the network. As opposed to fault-free networks, reaching agreement in the presence of Byzantine faults is far from trivial. In this paper, we propose a computationally-efficient algorithm that is provably robust to Byzantine faults. At each iteration of the algorithm, a good agent (1) performs a gradient descent update based on noisy local measurements, (2) exchanges its update with other agents in its neighborhood, and (3) robustly aggregates the received messages using coordinate-wise trimmed means. Under mild technical assumptions, we establish that good agents learn the true parameter asymptotically in almost sure sense. We further complement our analysis by proving (high probability) {\em finite-time} convergence rate, encapsulating network characteristics

Distributed Robust Bilinear State Estimation for Power Systems with Nonlinear Measurements

This paper proposes a fully distributed robust state-estimation (D-RBSE) method that is applicable to multi-area power systems with nonlinear measurements. We extend the recently introduced bilinear formulation of state estimation problems to a robust model. A distributed bilinear state-estimation procedure is developed. In both linear stages, the state estimation problem in each area is solved locally, with minimal data exchange with its neighbors. The intermediate nonlinear transformation can be performed by all areas in parallel without any need of inter-regional communication. This algorithm does not require a central coordinator and can compress bad measurements by introducing a robust state estimation model. Numerical tests on IEEE 14-bus and 118-bus benchmark systems demonstrate the validity of the method